Abstract We show that the universal minimal proximal flow and strongly of a discrete group can be realized as Stone spaces translation-invariant Boolean algebras subsets satisfying higher-order notion syndeticity. establish algebraic, combinatorial topological dynamical characterizations these we use to obtain new necessary sufficient conditions for strong amenability amenability. also characte...

in this paper we study the relation between module amenability of θ - lau product a×θb and that of banach algebras a, b. we also discuss module biprojectivity of a×θb. as a consequent we will see that for an inverse semigroup s, l 1 (s) ×θ l 1 (s) is module amenable if and only if s is amenable.

Let A $\mathcal {A}$ be a countable ℵ0-homogeneous structure. The primary motivation of this work is to study different amenability properties (subgroups of) the automorphism group Aut ( ) $\operatorname{Aut}(\mathcal {A})$ ; secondary existence weakly generic automorphisms . Among others, we present sufficient conditions implying invariant probability measures on certain subsets and also that ...

Liouville property of actions discrete groups can be reformulated in terms existence co-Følner sets. Since every action amenable group is Liouville, the used for proving non-amenability. There are many that defined by strongly transitive actions. In some cases amenability such an open problem. We define <mml:math xmlns:mml="http://www.w3.org/1998/Math...

Leptin’s theorem asserts that a locally compact group is amenable if and only if its Fourier algebra has a bounded (by one) approximate identity. In the language of locally compact quantum groups—in the sense of J. Kustermans and S. Vaes—, it states that a locally compact group is amenable if and only if its quantum group dual is co-amenable. It is an open problem whether this is true for gener...